If `a != 1 and l n a^(2) + (l n a^(2))^(2) + (l n a^(2))^(3) + ... = 3 (l n a + (l n a)^(2) + ( ln a)^(3) + (l n a)^(4) + ....)` then 'a' is equal to

ABCD is a square of lengths a, a in N, a gt 1 . Let L_(1),L_(2),L_(3) ... Be points BC such that BL_(1) = L_(1)L_(2) = L_(2)L_(3) = ....=1 and M_(1), M_(2), M_(3)... be points on CD such that CM_(1) = M_(1)M_(2) = M_(2)M_(3) = ...=1 .Then, sum_(n= 1)^(a-1)(AL_(n)^(2) + L_(n)M_(n)^(2)) is equal to

Subtract: 3l (l – 4 m + 5 n) from 4l ( 10 n – 3 m + 2 l )

Explain giving reasons which of the following sets of quantum number are not possible (a ) n=0, l =0 m_(l) = 0, m_(s ) =+ (1)/(2) ( b) n=1 , l = 0 m_(l) = 0, m_(s ) = - (1)/(2) ( c) n=1 , l = 1, m_(l ) = 0, m_(s ) = + (1)/(2) (d ) n= 2, l = 1, m_(l ) = 0, m_(s ) = (1) /(2) ( e) n=3, l = 3, m_(l) = 3, m_(s ) = + (1)/(2) (f ) n=3, l = 1, m_(l) = 0, m_(s) l = + (1)/(2)

|[(m+n)^(2), l^(2), mn], [(n+l)^(2), m^(2), ln], [(l+m)^(2), n^(2), lm]| =(l^(2) +m^(2) +n^(2))(l-m)(m-n)(n-l)(l+m+n)

Using the s,p,d notations, describe the orbital with the following quantum numbers : (a) n = 1, l = 0 " " (b) n = 3, l = 2 (c ) n = 3, l = 1 " " (d) n = 2, l = 1 (e ) n = 4, l = 3 " " (f) n = 4, l = 2 .